Which classifier should I use for a dataset with one feature?
It is not really a metter of what model, but if it is possible at all to predict what you're trying to predict. Let's take a similar dataset from kaggle: California Housing Prices 

This dataset contains house prices and other information among which the number of bedrooms per house. As suggested by Oliver in the comments we can compute the Person coefficient to estimate the correlation between the two variables. 

import pandas as pd
from scipy.stats import pearsonr

df = pd.read_csv('housing.csv')
df = df.apply(lambda row: row[df['total_bedrooms'] &lt;= 20]) # select subset of dataframe for sake of clarity
df.dropna(inplace=True)

x = df['median_house_value'] # our single feature  
y = df['total_bedrooms'] # target labels

print('Correlation: \n', pearsonr(x,y))


Out:

&gt;&gt;Correlation: 
&gt;&gt;(-0.14015312664251944, 0.12362969210761204)


The correlation is pretty low, which means that the price and number of bedrooms are basically not related. We can also plot the points to check that indeed there is no correlation at all.

df.plot(x='total_bedrooms',y='median_house_value',kind='scatter')


Out:



Training a model to predict the number of bedrooms uniquely from the price would mean to find a function that can interpolate all those points, which is an impossible task since we have several different prices for houses with the same amount of bedrooms. 

The only way to tackle a problem like this would be to expand the dimensionality of the data, for example by using a Support Vector Machine with a non linear kernel. But even with non linear kernels you can't do miracles, so if you're dataset looks like this one, the only solution would be to expand your dataset to include extra features.